Research in Coding Theory

I have just started learning about coding theory. Hence, I would like to ask for your suggestions and guidance for a very beginner like me.

1. Which books are good for beginning coding theory? (I start reading the notes by J.I. Hall from here).

2. Which topics now are hot in coding theory? so that I could look at and choose the track to follow.

3. Where I could find lastest preprints and papers on coding theory. I know only "Designs, Codes and Cryptography".

• Which aspect of coding theory you want? Engineering, Mathematics or Computer Science? Mar 13 '14 at 14:08
• alas asking about "hot research" is not gonna make any friends around here, however coincidentally RJLipton was just blogging about the intersection of coding theory & number theory specifically density of primes etc which is showing some recent attn/innovation. lots of leading refs there
– vzn
Mar 13 '14 at 18:33

From a mathematical perspective: Try

1) Handbook of coding theory - Huffman and Pless

2) Fundamentals of Error-Correcting Codes - Huffman and Pless

3) Introduction to coding theory - Ron Roth

4) Algebraic Geometric Codes: Basic Notions - Vladut, Nogin and Tsfasman

5) Introduction to Coding Theory - Van Lint

6) Algebraic Geometry in Coding Theory and Cryptography - Harald Niederreiter and Chaoping Xing.

From an engineering perspective: Try

1) Error Control Coding - Shu Lin and Daniel Costello

2) Modern Coding Theory - Richardson and Urbanke

3) Error Correction Coding - Todd K Moon

4) Channel Codes: Classical and Modern - William Ryan and Shu Lin.

From Computer Science perspective: Try

2) Algorithmic Results in List Decoding - Guruswami

3) Computational complexity - Boaz Barak (Chapter 19)

4) Refer this cstheory question - Using error-correcting codes in theory

5) Locally Decodable Codes - Yekhanin

6) Chapter on applications of coding theory in complexity theory in Different Aspects of Coding Theory - Calderbank.

Lecture notes of the course "An Algorithmic Introduction to Coding Theory," by Madhu Sudan. Publication Date: 2001. The first chapter offers useful comments regarding several textbooks on coding theory. Available at http://people.csail.mit.edu/madhu/FT01/scribe/overall.pdf.

My favorites for the first part of your question:

Neal Koblitz: "A Course in Number Theory and Cryptography"
$\rightarrow$ Very good introduction for mathematical treatment

Oded Goldreich: "The Foundations of Cryptography"
$\rightarrow$ More applications, but also a good book for basical interests

Thomas M. Cover and Joy A. Thomas: "Elements of Information Theory"
$\rightarrow$ This book presents a great overview about the whole package of information theory

Imre Csiszár and János Körner: "Information Theory: Coding Theorems for Discrete Memoryless Systems"
$\rightarrow$ Anonther classic for information theory

Jörg Rothe: "Complexity theory and cryptology"
$\rightarrow$ This book focussing on the complexity aspects (like the name already says)

• How does Koblitz and Goldreich books contribute to starting coding theory? I don't know about others, but I studied these books and I strongly believe there's no correlation between them and beginning coding theory. Mar 13 '14 at 3:06
• I would think Danny has suggested some books for beginners in both cryptography and Information Theory. Any suggestions are highly appreciated.^^
– 9999
Mar 13 '14 at 6:31
• These are indeed very nice books to study if you are working on Cryptography, however, for topics in coding theory I am just not too sure about the first two books (having read them), why not ALSO take a look at notes from course offerings from Venkat Guruswami (CMU) or Atri Rudra (UBuffalo). Mar 13 '14 at 7:25
• Maybe i overestimate the relevance of cryptography in this question.. :) Mar 13 '14 at 7:34

excellent 50p survey by leading expert/member Luca Trevisan from 2004 also tracking recent/latest research in the field

sections:

1. Introduction
2. Error-Correcting codes
3. Sublinear Time Unique Decoding
4. Sublinear Time List Decoding
5. Locally Testable Codes